Simplified model analysis simulation method considering internal and external interaction of infilled wall plane at different stages

Abstract

The invention discloses a simplified model analysis simulation method considering internal and external interaction of an infilled wall plane at different stages. The method comprises the following steps: 1, determining nodes of peripheral vertical and horizontal structural members, end points and middle nodes of a middle elastic-plastic supporting rod of an infilled wall and local nodes of the horizontal structural members; 2, constructing a simplified model of the filler wall; 3, fiber discretization is carried out on an elastic-plastic supporting rod in the middle of the filler wall, and coupling earthquake response inside and outside the plane of the filler wall is analyzed; 4, dividing different damage states of the filler wall, and proposing an interaction relationship between the inside and outside of the plane of the filler wall in different damage states; and 5, calculating an interaction curve of the filler wall in different damage states. The problem that parameters such as fiber area and distance in a simplified model are difficult to dynamically adapt to pain points of different injury states is solved, synchronous matching of mechanical parameters and the injury states in the simulation process is ensured, and the result accuracy is improved.

Description

Technical Field

[0001] This invention belongs to the field of seismic construction of buildings and relates to a simplified analysis and simulation method for infill walls. Specifically, it relates to a simplified model analysis and simulation method that considers the interaction between the infill walls inside and outside the plane at different stages. Background Technology

[0002] In the field of building structures, infill walls, as important non-structural components in frame structures, have always been a hot research topic due to their load-bearing performance and interaction with the main structure. Especially under complex loads, the coupling relationship between out-of-plane and in-plane loads on infill walls, and the resulting deterministic interaction mechanism between in-plane and out-of-plane displacements, are crucial for accurately assessing the safety and stability of structures under extreme seismic conditions. Currently, although some scholars have begun to focus on and engage in this research area, conducting preliminary discussions on the interaction between in-plane and out-of-plane displacement limits of rigidly connected infill walls under specific damage states, most of these studies are limited to specific damage states, load types, or boundary conditions, lacking research on the in-plane and out-of-plane interaction relationships of infill walls with different degrees of damage. Summary of the Invention

[0003] To address the problem that existing simulation methods cannot accurately account for the coupling of seismic performance between the in-plane and out-of-plane areas of infill walls, this invention provides a simplified model analysis and simulation method that considers the interaction between the in-plane and out-of-plane areas of infill walls at different stages, applicable to the analysis of the coupled seismic response between the in-plane and out-of-plane areas of infill walls.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] A simplified model analysis and simulation method considering the in-plane and out-of-plane interactions of infill walls at different stages includes the following steps:

[0006] Step 1: Determine nodes 1, 2, 3, and 4 of the surrounding vertical and horizontal structural members; divide the elasto-plastic strut in the middle of the infill wall into two elasto-plastic struts with out-of-plane degrees of freedom bound to the intermediate nodes, and determine the four endpoints and two intermediate nodes of the elasto-plastic strut in the middle of the infill wall: endpoint 5, endpoint 6, endpoint 7, endpoint 8, intermediate node 9, and intermediate node 10; determine the local nodes 24, 25, 26, and 27 of the horizontal structural members;

[0007] Step 2: Connect node 1 and node 2 to form structural member 11; connect node 3 and node 4 to form structural member 13; connect node 2 and node 3 to form structural member 12; connect endpoint 5, intermediate node 9, and endpoint 8 to form the intermediate elastic-plastic strut 22 of the infill wall; connect endpoint 7, intermediate node 10, and endpoint 6 to form the intermediate elastic-plastic strut 23 of the infill wall; connect node 2 and endpoint 5 to form the rigid strut 14 of the infill wall; connect endpoint 5 and local node 25 to form the rigid strut 15 of the infill wall; connect node 4 and endpoint 8 to form the rigid strut of the infill wall. Stiffener 16 connects local node 26 and endpoint 8 to form rigid stiffener 17 for the infill wall; local node 24 connects local node 24 and endpoint 6 to form rigid stiffener 18 for the infill wall; node 3 connects node 3 and endpoint 6 to form rigid stiffener 19 for the infill wall; node 1 connects node 1 and endpoint 7 to form rigid stiffener 20 for the infill wall; and local node 27 connects local node 27 and endpoint 7 to form rigid stiffener 21 for the infill wall, thus obtaining a simplified model of the infill wall. Section and material properties are assigned to structural members 11, 12, and 13, and boundary conditions, mass, and loads are assigned to the simplified model of the infill wall.

[0008] Step 3: Discretize the fibers of the elastoplastic struts in the middle of the infill wall. Each fiber represents a small area on the cross section with different positions, cross-sectional areas and material properties. Analyze the coupled seismic response of the infill wall inside and outside the plane.

[0009] Step 4: Classify the infill wall into different damage states and propose the interaction relationship between the infill wall inside and outside the plane under different damage states;

[0010] Step 5: Calculate the interaction curves of the infill wall under three different damage states.

[0011] Compared with the prior art, the present invention has the following advantages:

[0012] 1. This invention covers the interaction study of different damage stages: It overcomes the shortcomings of existing technologies that are limited to specific damage states. By establishing the interaction relationship between the bearing capacity inside and outside the plane under each of the three clearly defined damage states of slight, moderate and severe (yield, peak and residual), it reflects the changes in mechanical behavior during the damage evolution process of the infill wall.

[0013] 2. In this invention, the strut is under compression regardless of whether the force is applied from left to right or from right to left, which better reflects the actual compression state of the infill wall under earthquake action.

[0014] 3. This invention achieves unified and accurate simulation of in-plane and out-of-plane forces: Through the model design of "8 rigid struts + 2 elastic-plastic struts bound to out-of-plane degrees of freedom", the elastic-plastic struts can simultaneously bear axial pressure and bending deformation, matching the in-plane axial bearing capacity, and through equivalent mass (81% of the self-weight of the infill wall) and bending bearing capacity calibration, ensuring that the out-of-plane mechanical properties are consistent with reality, thus solving the problem that existing models cannot take into account the two-way load coupling.

[0015] 4. Overcoming the challenge of dynamic parameter adjustment: The innovative method of "approximating different curvature curves with the same slope broken line" solves the problem that parameters such as fiber area and distance in the simplified model are difficult to dynamically adapt to different damage states (curvature changes), ensuring that mechanical parameters and damage states are synchronously matched during the simulation process and improving the accuracy of the results. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the infill wall and the intermediate elastic-plastic strut;

[0017] Figure 2 This is a schematic diagram of fiber discreteness;

[0018] Figure 3 Simplified in-plane load-displacement curves for infill walls;

[0019] Figure 4 Assignment diagram of interaction relationship curves;

[0020] Figure 5 These are the in-plane and out-of-plane interaction curves under different damage states. Detailed Implementation

[0021] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0022] This invention provides a simplified model analysis and simulation method for infill walls that consider in-plane and out-of-plane interactions at different stages. The method includes the following steps:

[0023] Step 1: Determine nodes 1, 2, 3, and 4 of the surrounding vertical and horizontal structural members; divide the elasto-plastic strut in the middle of the infill wall into two elasto-plastic struts with out-of-plane degrees of freedom bound to the intermediate nodes, and determine the four endpoints and two intermediate nodes of the elasto-plastic strut in the middle of the infill wall: endpoint 5, endpoint 6, endpoint 7, endpoint 8, intermediate node 9, and intermediate node 10. Among them, endpoint 5 and endpoint 7 are in the same position, endpoint 6 and endpoint 8 are in the same position, and intermediate node 9 and intermediate node 10 are in the same position; determine the local nodes 24, 25, 26, and 27 of the horizontal structural members.

[0024] In this step, the method for determining the positions of endpoints 5, 6, 7, 8, intermediate node 9, intermediate node 10, local node 24, local node 25, local node 26, and local node 27 is as follows: the angle between the line connecting node 2 and endpoint 5 and the line connecting node 2 and node 1 is 30-45 degrees; the angle between the line connecting node 1 and endpoint 7 and the line connecting node 1 and node 2 is 30-45 degrees; the angle between the line connecting node 3 and endpoint 6 and the line connecting node 3 and node 4 is 30-45 degrees; the angle between the line connecting node 4 and endpoint 8 and the line connecting node 4 and node 3 is 30-45 degrees; intermediate node 9 is set at the midpoint of the line connecting endpoint 5 and endpoint 8; intermediate node 10 is set at the midpoint of the line connecting endpoint 6 and endpoint 7; the distances between local nodes 24, 25, 26, and 27 and nodes 2, 3, 1, and 4 are respectively within 30% of the length of the horizontal structural member.

[0025] Step 2: Connect node 1 and node 2 to form structural member 11; connect node 3 and node 4 to form structural member 13; connect node 2 and node 3 to form structural member 12; connect endpoint 5, intermediate node 9, and endpoint 8 to form intermediate elastic-plastic strut 22 of the infill wall; connect endpoint 7, intermediate node 10, and endpoint 6 to form intermediate elastic-plastic strut 23 of the infill wall; connect node 2 and endpoint 5 to form rigid strut 14 of the infill wall; connect endpoint 5 and local node 25 to form rigid strut 15 of the infill wall; connect node 4 and endpoint 8 to form rigid strut 16 of the infill wall; connect local node 26 and endpoint 8 to form rigid strut 17 of the infill wall; connect local node 24 and endpoint 6 to form rigid strut 18 of the infill wall; connect node 3 and endpoint 6 to form rigid strut 19 of the infill wall; connect node 1 and endpoint 7 to form rigid strut 20 of the infill wall; connect local node 27 and endpoint 7 to form rigid strut 21 of the infill wall, thus obtaining a simplified model of the infill wall. Assign cross-sections and material properties to structural members 11, 12, and 13, and assign boundary conditions, mass, and loads to the model.

[0026] In this step, the simplified model of the infill wall consists of 8 rigid infill wall struts and 2 intermediate elastic-plastic struts. One node of each of the 8 rigid infill wall struts is a structural member node, and the other node connects to the end point of the intermediate elastic-plastic strut. The intermediate elastic-plastic strut is divided into two elastic-plastic struts that bind the out-of-plane degrees of freedom of the intermediate node, as shown below. Figure 1 As shown in the figure. Among them, the elastic-plastic strut in the middle of the infill wall can not only withstand axial pressure, but also simulate bending deformation, so as to realize a unified description of the in-plane and out-of-plane effects of the infill wall, thereby more accurately simulating the nonlinear stress behavior of the infill wall.

[0027] Step 3: Discretize the fibers of the elasto-plastic struts in the middle of the infill wall. Each fiber represents a small area on the cross section with different positions, cross-sectional areas and material properties. Analyze the coupled seismic response of the infill wall inside and outside the plane.

[0028] In this step, such as Figure 2 As shown, the method for fiber discretization of the elasto-plastic struts in the middle of the infill wall is as follows:

[0029] like Figure 1 As shown, when the infill wall is subjected to an in-plane load from left to right, the rigid struts of the blue infill wall are under compression, while the rigid struts of the red infill wall are not under load. In this case, the beam-column elements at the center are under compression. Conversely, when the infill wall is subjected to an in-plane load from right to left, the rigid struts of the red infill wall are under compression, and the beam-column elements at the center are still under compression, thus simulating the compression state of the infill wall under seismic loading. To ensure that the simplified model accurately reflects the mechanical properties of the infill wall under purely in-plane loads, the in-plane force-displacement relationship of the infill wall needs to be simplified, and the axial force-displacement relationship of the elasto-plastic struts in the middle of the infill wall needs to be determined through geometric transformation.

[0030] Calculate the in-plane bearing capacity of the simplified model of the infill wall :

[0031] (1)

[0032] (2)

[0033] (3)

[0034] In the formula: In-plane bearing capacity; For horizontal shearing capacity; This refers to the area of ​​the masonry infill. This refers to the thickness of the infill wall; This is the length of the infill wall; For the shear strength of the masonry; The expected weight of the wall panel.

[0035] The out-of-plane stress characteristics of the infill wall are reflected by the out-of-plane bending of the elasto-plastic strut in the middle of the infill wall. When an out-of-plane force is applied at the central node, the elasto-plastic strut in the middle of the infill wall becomes particularly important, as it determines the bending stiffness and failure mode of the wall. To accurately depict the mechanical behavior of the infill wall under purely out-of-plane loads, it is crucial to ensure that the maximum out-of-plane bending capacity of the elasto-plastic strut in the middle of the infill wall matches the actual out-of-plane load capacity of the infill wall. Simultaneously, under this condition, the deflection at the center point of the elasto-plastic strut in the middle of the infill wall should also be consistent with the out-of-plane displacement at the center point of the infill wall. Given that the simplified model of the infill wall can be considered as a simply supported beam with concentrated mass at mid-span in the out-of-plane direction, while the actual infill wall system behaves as a simply supported beam with distributed mass, to achieve the equality of their first-order natural frequencies, the equivalent mass of the infill wall at the central node of the simplified model is adjusted to 81% of the infill wall's self-weight.

[0036] Determine the out-of-plane bending capacity of the elastoplastic struts in the middle of the infill wall:

[0037] In this case, the relationship between the out-of-plane flexural capacity of the simplified model of the infill wall and the out-of-plane flexural capacity of the infill wall is as follows:

[0038] (4)

[0039] (5)

[0040] (6)

[0041] In the formula, The out-of-plane flexural capacity of the infill wall is simplified in the model. To simplify the model length for infill walls; This refers to the out-of-plane flexural capacity of the infill wall. This refers to the height of the infill wall; For out-of-plane uniformly distributed loads on the infill wall; The compressive strength of the masonry; Take 0.04.

[0042] Determine the moment of inertia of the cross section of the elastoplastic strut in the middle of the infill wall:

[0043] Based on the relationship between the deflection at the center point of the simplified infill wall model (i.e., the bending deformation of the simplified infill wall model) and the secant stiffness corresponding to the out-of-plane bearing capacity of the infill wall, the relationship between the out-of-plane moment of inertia and the secant stiffness of the simplified infill wall model can be established:

[0044] (7)

[0045] (8)

[0046] (9)

[0047] (10)

[0048] (11)

[0049] (12)

[0050] (13)

[0051] In the formula, Let be the moment of inertia of the cross section of the elastic-plastic strut in the middle of the infill wall; The secant stiffness is the out-of-plane bearing capacity of the infill wall. The elastic modulus of the infill wall; Out-of-plane effective weight; This represents the total weight of the infill wall. For heavy-duty infill walls; This is the first-order vibration frequency of the infill wall; It is the acceleration due to gravity; The moment of inertia of the infill wall section in its initial cracked state; This refers to the weight per unit length of the infill wall.

[0052] To simulate the in-plane and out-of-plane interaction of an infill wall under bidirectional loads, the cross-section of the elasto-plastic strut in the simplified model of the infill wall was meticulously designed. In the out-of-plane direction, the cross-section of the elasto-plastic strut was discretized into n fibers, each fiber representing a specific small region on the cross-section, with different locations, cross-sectional areas, and material properties. This design allows the invention to more accurately capture and describe the mechanical response of the infill wall under complex load conditions. Under the combined action of in-plane and out-of-plane loads, the plastic neutral axis of the elasto-plastic strut cross-section dynamically changes, particularly in the out-of-plane direction. This directly leads to corresponding changes in its in-plane axial bearing capacity and out-of-plane flexural bearing capacity. This change is a direct manifestation of the in-plane and out-of-plane interaction of the infill wall. As the axial force on the elasto-plastic strut cross-section gradually increases, the neutral axis tends to move towards the compressed side. This movement further affects the stress distribution of each fiber, potentially leading to a decrease in the overall flexural bearing capacity of the cross-section. Similarly, changes in the bending moment on the cross-section of the elasto-plastic strut in the middle of the infill wall also significantly affect the stress-strain state of each fiber. This process of mutual influence and dynamic adjustment allows the present invention to more comprehensively understand and predict the overall mechanical properties of the infill wall under complex loading conditions. In summary, by discretizing the cross-section of the elasto-plastic strut in the middle of the infill wall and considering the combined effects of in-plane and out-of-plane loads, the in-plane and out-of-plane interactions of the infill wall can be simulated more accurately, providing strong support for structural design and analysis.

[0053] Determine the fiber parameters after discretizing the cross-section of the elasto-plastic strut in the middle of the infill wall:

[0054] The in-plane axial bearing capacity of the infill wall under in-plane and out-of-plane loads out-of-plane flexural capacity The interaction curve between the fibers can determine the position and peak load capacity of each fiber. The calculation formula is as follows:

[0055] (14)

[0056] (15)

[0057] In the formula, For a discrete point sequence, when When =1, - The out-of-plane bending moment on the interaction curve is 0; For the first Peak load-bearing capacity of root fibers; for - The first interaction curve The in-plane axial bearing capacity at each discrete point; For the first The distance between the root fiber and the center of the wall section in the out-of-plane direction; for - The first interaction curve Out-of-plane flexural capacity at discrete points.

[0058] Therefore, the peak stress and peak strain of each fiber can be calculated according to equations (16) and (17):

[0059] (16)

[0060] (17)

[0061] In the formula, For the first Peak stress of the root fiber; For the first The area of ​​the root fiber; For the first Peak strain of the root fiber.

[0062] The cross-sectional area of ​​the discretized fibers needs to meet the following requirements: 1) The sum of the areas of all fibers is consistent with the cross-sectional area of ​​the elasto-plastic strut in the middle of the infill wall; 2) The moment of inertia of the discretized fiber cross-section is the same as that of the elasto-plastic strut in the middle of the infill wall. The cross-sectional area of ​​each fiber can be obtained by simultaneously solving the following equations:

[0063] (18)

[0064] (19)

[0065] In the formula, for The number of fibers on one side of the axis; The thickness of the infill wall; This refers to the width of the elastic-plastic strut in the middle of the infill wall.

[0066] Step 4: The infill wall exhibits different behaviors under different damage states. This step categorizes the infill wall into different damage states and proposes the in-plane and out-of-plane interaction relationships under these different damage states.

[0067] The in-plane and out-of-plane interactions of an infill wall exhibit significant differences as it undergoes different damage states. When the infill wall is slightly damaged, the influence of in-plane forces on out-of-plane deformation is not significant, and the interaction between the two is weak. Out-of-plane deformation is more controlled by its own out-of-plane loads and boundary conditions. However, as the damage gradually worsens, when the infill wall enters a moderately damaged state, the stress redistribution within the wall caused by in-plane forces begins to significantly affect the out-of-plane mechanical behavior. In-plane and out-of-plane deformations become coupled to some extent, and the interaction gradually strengthens. When the infill wall reaches a severely damaged state or is even on the verge of collapse, the in-plane and out-of-plane interactions become highly complex. The propagation of in-plane cracks and nonlinear deformation of the material greatly alter the out-of-plane load-bearing and deformation characteristics. The mechanical responses inside and outside the plane are closely intertwined, and the interaction relationship has fundamentally changed compared to the slightly damaged state.

[0068] From the perspective of damage development patterns and mechanical properties of infill walls, there is a close and specific correspondence between different damage states and load-bearing capacity states. Typically, when an infill wall is in a state of slight damage, its in-plane and out-of-plane strength has reached the yield level. This means that at this damage stage, the infill wall's performance in terms of axial force in the in-plane and flexural force in the out-of-plane begins to change significantly. In other words, the load-bearing capacity and deformation capacity exhibited by the infill wall in the state of slight damage are similar to, and equivalent to, the mechanical properties exhibited in the yield state. When the infill wall further develops to a state of moderate damage, its in-plane and out-of-plane strengths reach their peak values. This stage signifies that the infill wall has reached its performance limit in resisting loads, and its load-bearing capacity has reached its maximum. The peak value corresponding to the state of severe damage clearly defines the load-bearing limit of the infill wall within the normal stress range, providing a crucial basis for subsequent failure assessment. Furthermore, there is a direct correspondence between the failure state and the collapse state of the infill wall. The collapse state is the final failure form of the infill wall under load, representing that the structure has completely lost its load-bearing capacity and stability. When the infill wall reaches a state of collapse, it means that it has entered a state of failure.

[0069] Therefore, the interaction between the in-plane axial bearing capacity and the out-of-plane flexural bearing capacity of the simplified model of the infill wall can be expressed as follows:

[0070] yield:

[0071] (20)

[0072] Peak value:

[0073] (twenty one)

[0074] Residue:

[0075] (twenty two)

[0076] In the formula, The in-plane axial bearing capacity of the simplified model of the infill wall in its current state; Out-of-plane flexural capacity of the simplified model of the infill wall under the current condition; The in-plane yield point bearing capacity of a simplified model of an infill wall under pure in-plane load; The out-of-plane yield point flexural bearing capacity of a simplified model of an infill wall under pure out-of-plane load; The in-plane peak bearing capacity of a simplified model of an infill wall under pure in-plane load; The out-of-plane peak flexural capacity of a simplified model of an infill wall under pure out-of-plane load. The in-plane residual point bearing capacity of a simplified model of an infill wall under pure in-plane load; The out-of-plane residual bending capacity of the infill wall under a simplified model of pure out-of-plane load.

[0077] The in-plane forces on the infill wall can be simplified to the compression of an equivalent strut. To calibrate this equivalent strut, the simplified in-plane load-displacement curve of the infill wall is first needed, such as... Figure 3 As shown. In the simplified in-plane load-displacement curve, the in-plane stress behavior of the infill wall can be described by the following three characteristic points:

[0078] (1) Yield point: indicates that the infill wall begins to yield and its stiffness changes;

[0079] (2) Peak point: represents the maximum bearing capacity of the infill wall under in-plane load;

[0080] (3) Failure point: indicates the final failure of the infill wall.

[0081] By determining the yield point, peak point, and failure point, a simplified load-displacement curve of the equivalent diagonal strut of the infill wall is constructed. This allows for the further construction of the stress-strain relationship of each fiber beam element in the equivalent diagonal strut of the infill wall, enabling the simplified model to accurately simulate the in-plane stress performance of the infill wall.

[0082] The relationship between yield strength and corresponding in-plane displacement can be expressed as follows:

[0083] (twenty three)

[0084] (twenty four)

[0085] The relationship between peak intensity and corresponding in-plane displacement can be expressed as follows:

[0086] (25)

[0087] (26)

[0088] The relationship between residual strength and corresponding in-plane displacement can be expressed as follows:

[0089] = 0.85 (27)

[0090] (28)

[0091] In the formula, Yield strength; Peak intensity; Residual strength; This represents the in-plane displacement corresponding to the yield strength. This represents the in-plane displacement corresponding to the peak intensity. This represents the in-plane displacement corresponding to the residual strength. For axial stiffness; The stiffness of the reinforced segment of the equivalent strut load-displacement curve for the infill wall; The angle between the infill wall struts.

[0092] Step 5: Calculate the interaction curves of the infill wall under three different damage states.

[0093] In the analysis of the simplified model of infill walls, a tricky problem arises when dealing with variations in curvature. These three curves each have a unique distribution of load-bearing capacity or bending moment, and their allocated areas and fiber cross-section distances change with curvature. However, in the established simplified model, the key parameters such as the area and distance of the fiber cross-section elements are determined at the start of the simulation. During the simulation, it is difficult to dynamically change the area and distance of these fibers, making it difficult to accurately simulate the actual mechanical behavior of the structure under different curvature variations, i.e., different damage states, thus affecting the accuracy of the simulation results. Essentially, it's the reciprocal of the slope of the secant line in the PM interaction curve. This means the problem can be transformed into how to approximate the curve using a secant line. Specifically, it involves using a series of broken lines with the same slope to represent curves with different curvatures, in order to achieve a more reasonable simulation of mechanical properties in a simplified model.

[0094] Therefore, to address the above problems, this invention proposes an effective solution, the specific process of which is as follows:

[0095] Step 1: Segment the yield curve and calculate the slope of the broken line. First, select the curve with the largest curvature from the three curves in equations (20), (21), and (22), which is the curve corresponding to the yield state of the structure, i.e., equation (20). In the first quadrant, divide the curve evenly into segments according to the specified angle. part, Take an odd number, and the angle of each segment is... .by As the x-axis, y is the vertical axis, where For in-plane loads, For in-plane peak load, The out-of-plane bending moment, This represents the maximum out-of-plane bending moment. The result is obtained by calculating the slope of each segment of the broken line. slope of the broken line ( =1,2,⋯), such as Figure 4 As shown.

[0096] (29)

[0097] Step 2: Determine the segmentation points of the other two curves based on the slope of the broken line of the yield curve. After obtaining the slope of the broken line of the yield curve... Then, these slopes are used to derive the curves step by step from both ends towards the middle. That is, while keeping the slopes constant, points on the other two curves are connected sequentially from both ends towards the middle to determine the segmentation points of the other two curves. This method ensures that all three curves have the same slope within their corresponding segmented intervals. Figure 5 As can be seen intuitively, the broken line obtained in this way can approximately represent three curves with different curvatures, while ensuring that their slopes are equal in corresponding segments.

[0098] Step 3: Calculate the actual load, bending moment, and distance. After determining the segmentation points and corresponding slopes of the three curves, multiply them by the load. and reference bending moment The actual load can then be obtained. and actual bending moment ( =1,2,...). With the actual load and bending moment values, we can further calculate parameters such as the fiber cross-sectional area allocated to the corresponding curve and the stress and strain of the structure at different locations.

[0099] Example:

[0100] This embodiment provides a single-story, single-span reinforced concrete frame with a story height of 1700mm, a span of 2300mm, an infill wall thickness of 100mm, a height of 1400mm, a width of 2100mm, and a length of 1045mm for the elastic-plastic strut in the middle of the infill wall.

[0101] Step 1: In the OpenSees finite element software, create the corresponding reinforced concrete frame model by defining geometric parameters, defining node coordinates, defining beam and column sections, defining beam and column elements, and defining loads.

[0102] Step 2: Simplify the in-plane bearing capacity of the infill wall model Perform calculations, where It is 0.23 MPa. Take 50kN.

[0103] Step 3: Calculate the out-of-plane bending capacity of the simplified model of the infill wall strut. The resultant force of the uniformly distributed out-of-plane load is 60kN. The out-of-plane bending capacity of the simplified model of the infill wall is thus obtained.

[0104] Step 4: Calculate the out-of-plane moment of inertia of the simplified infill wall model, where the elastic modulus is 1260 MPa. The calculated out-of-plane moment of inertia is 5887.47 cm. 4 .

[0105] Step 5: The curve was divided into 9 segments according to angles of 10 degrees, 20 degrees, 30 degrees, 40 degrees, 50 degrees, 60 degrees, 70 degrees, 80 degrees, and 90 degrees. As the x-axis, Using the vertical axis as the ordinate, the slope of each segment of the broken line is calculated to obtain... slope of the broken line ( =1,2,...,9). After determining the slope, multiply it by the load respectively. and reference bending moment The actual load can then be obtained. and actual bending moment ( =1,2,...,9). With the actual load and bending moment values, we can further calculate the fiber cross-sectional area allocated to the corresponding curve, the stress and strain of the structure at different locations, and other parameters, as shown in Tables 1-3.

[0106]

[0107]

[0108]

[0109] In summary, by using the above-mentioned method of approximating curves with different curvatures using broken lines with the same slope, the difficulty of dynamically changing the fiber area and distance in the simplified model can be overcome to a certain extent. This allows for a more accurate simulation of the mechanical properties of the structure under different curvature variations, providing strong support for the analysis and design of the simplified model of infill walls.

Claims

1. A simplified model analysis simulation method considering the in-plane and out-of-plane interaction of different stage infill walls, characterized in that The method comprises the following steps: Step one: determine the nodes 1, 2, 3, 4 of the peripheral vertical and horizontal structural members, divide the intermediate elastic-plastic bracing rods in the infilled wall into two elastic-plastic bracing rods for binding the intermediate nodes out of the plane, determine the four end points and two intermediate nodes of the intermediate elastic-plastic bracing rods in the infilled wall, i.e. the end points 5, 6, 7, 8, the intermediate nodes 9 and 10, and determine the local nodes 24, 25, 26, 27 of the horizontal structural members; Step two: connect the nodes 1 and 2 to form a structural member 11, connect the nodes 3 and 4 to form a structural member 13, connect the nodes 2 and 3 to form a structural member 12, connect the end points 5, 8 and the intermediate node 9 to form an intermediate elastic-plastic bracing rod 22 of the infilled wall, connect the end points 7, 6 and the intermediate node 10 to form an intermediate elastic-plastic bracing rod 23 of the infilled wall, connect the node 2 and the end point 5 to form a rigid bracing rod 14 of the infilled wall, connect the end point 5 and the local node 25 to form a rigid bracing rod 15 of the infilled wall, connect the node 4 and the end point 8 to form a rigid bracing rod 16 of the infilled wall, connect the local node 26 and the end point 8 to form a rigid bracing rod 17 of the infilled wall, connect the local node 24 and the end point 6 to form a rigid bracing rod 18 of the infilled wall, connect the node 3 and the end point 6 to form a rigid bracing rod 19 of the infilled wall, connect the node 1 and the end point 7 to form a rigid bracing rod 20 of the infilled wall, connect the local node 27 and the end point 7 to form a rigid bracing rod 21 of the infilled wall, and obtain a simplified model of the infilled wall; the structural members 11, 12, 13 are endowed with cross-section and material properties, and the simplified model of the infilled wall is endowed with boundary conditions, mass and load; Step three: perform fiber discretization on the intermediate elastic-plastic bracing rods of the infilled wall, each fiber represents a small area on the cross-section and has different positions, cross-sectional areas and material properties, and analyze the in-plane and out-of-plane coupling seismic response of the infilled wall; Step four: divide the infilled wall into different damage states, and propose the interaction relationship between the in-plane and out-of-plane of the infilled wall under different damage states; Step five: calculate the interaction curves of the infilled wall under three different damage states.

2. The method according to claim 1, wherein the method is characterized by In step one, the method for determining the positions of the end points 5, 6, 7, 8, the intermediate nodes 9, 10, the local nodes 24, 25, 26, 27 is as follows: the angle between the line connecting the node 2 and the end point 5 and the line connecting the node 2 and the node 1 is 30-45 degrees, the angle between the line connecting the node 1 and the end point 7 and the line connecting the node 1 and the node 2 is 30-45 degrees, the angle between the line connecting the node 3 and the end point 6 and the line connecting the node 3 and the node 4 is 30-45 degrees, and the angle between the line connecting the node 4 and the end point 8 and the line connecting the node 4 and the node 3 is 30-45 degrees; the intermediate node 9 is arranged at the middle position of the line connecting the end points 5 and 8, and the intermediate node 10 is arranged at the middle position of the line connecting the end points 6 and 7; the distances between the local nodes 24, 25, 26, 27 and the nodes 2, 3, 1, 4, respectively, are within 30% of the length of the horizontal structural member.

3. The method according to claim 1, wherein the method is characterized by The method for fiber discretization of the elastic-plastic strut in the middle of the infilled wall in step three is as follows: (1) Calculate the in-plane bearing capacity of the nine-brace simplified model of the infilled wall : wherein: is the in-plane load capacity; is the horizontal shear capacity; is the masonry infill area; is the infill wall thickness; is the infill wall length; is the masonry shear strength; is the wall panel expected gravity; (2) Determine the out-of-plane bending capacity of the elastic-plastic strut in the middle of the infilled wall: The relationship between the out-of-plane bending capacity of the nine-strut simplified model of the infilled wall and the out-of-plane bending capacity of the infilled wall is as follows: In the formula, is the out-of-plane bending capacity of the nine-strut simplified model of the infilled wall; is the length of the nine-strut simplified model of the infilled wall; is the out-of-plane bending capacity of the infilled wall; is the height of the infilled wall; (3) Determine the sectional moment of inertia of the elastic-plastic strut in the middle of the infilled wall: According to the relationship between the central point deflection of the nine-strut simplified model of the infilled wall, i.e. the bending deformation of the nine-strut simplified model of the infilled wall, and the secant stiffness corresponding to the out-of-plane bearing capacity of the infilled wall, the relationship between the out-of-plane directional moment of inertia of the nine-strut simplified model of the infilled wall and the secant stiffness is established: In the formula, is the sectional moment of inertia of the elastic-plastic strut in the middle of the infilled wall; is the secant stiffness corresponding to the out-of-plane bearing capacity of the infilled wall; is the elastic modulus of the infilled wall; (4) In the out-of-plane direction, the cross section of the elastic-plastic strut in the middle of the infilled wall is discretized into n fibers, each fiber representing a specific small area on the cross section, and these areas have different positions, cross-sectional areas and material properties; (5) Determine the fiber parameters after the cross section of the elastic-plastic strut in the middle of the infilled wall is discretized: The interaction relationship curve between the in-plane axial bearing capacity and the out-of-plane bending bearing capacity of the infilled wall under in-plane and out-of-plane loads is determined, and the position and peak strength of each fiber are determined according to the following formula: and the out-of-plane bending bearing capacity ​ wherein is the sequence of discrete points, when = 1, - the out-of-plane bending moment on the interaction curve is zero; is the first peak load capacity of the root fiber; is the - the in-plane axial load capacity at the discrete point on the interaction curve; is the first distance of the root fiber from the center of the wall section in the out-of-plane direction; - the out-of-plane bending load capacity at the discrete point on the interaction curve; Therefore, the peak stress and peak strain of each fiber are calculated according to the following formula: wherein the peak stress of the first root fiber; the area of the first root fiber; the peak strain of the first root fiber; (6) By solving the following formula, the cross-sectional area of each fiber is obtained: wherein is the number of fibers on one side of the shaft; is the thickness of the infill wall; is the width of the elastic-plastic strut in the middle of the infill wall.

4. The method according to claim 3, wherein the method is characterized by In the (2), the formula for calculating the out-of-plane bending load capacity of the infill wall is as follows: In the (2), the formula for calculating the out-of-plane bending load capacity of the infill wall is as follows: wherein is the out-of-plane uniform load of the infill wall; is the compressive strength of the masonry; is taken as 0.

04.

5. The method of claim 3, wherein the method is characterized by In the (3), the formula for calculating the secant stiffness corresponding to the out-of-plane bearing capacity of the infilled wall is as follows: The formula is as follows. wherein is the total weight of the infill wall; is the specific weight of the infill wall; is the first order frequency of the infill wall; is the acceleration due to gravity; is the moment of inertia of the infill wall in its initial cracked state; is the weight per unit length of the infill wall.

6. The method of claim 3, wherein the method is characterized by In the (6), the cross-sectional area of the discretized fiber needs to meet the following requirements: 1) The sum of the areas of the fibers is consistent with the cross-sectional area of the elastic-plastic strut in the middle of the infilled wall; 2) The sectional moment of inertia of the discretized fiber is the same as that of the elastic-plastic strut in the middle of the infilled wall.

7. The method of claim 1, wherein the method is characterized by In step four, the interaction relationship between the in-plane axial bearing capacity and the out-of-plane bending capacity of the simplified model of the infilled wall is represented as follows: Yield: (1) Peak: (2) Residual: (3) wherein is the in-plane axial load capacity of the current state of the infilled wall simplified model; is the out-of-plane flexural load capacity of the current state of the infilled wall simplified model; is the in-plane yield point load capacity of the infilled wall simplified model under pure in-plane loading; is the out-of-plane yield point flexural load capacity of the infilled wall simplified model under pure out-of-plane loading; is the in-plane peak point load capacity of the infilled wall simplified model under pure in-plane loading; is the out-of-plane peak point flexural load capacity of the infilled wall simplified model under pure out-of-plane loading; is the in-plane residual point load capacity of the infilled wall simplified model under pure in-plane loading; is the out-of-plane residual point flexural load capacity of the infilled wall simplified model under pure out-of-plane loading; The relationship between the yield strength and the corresponding in-plane displacement is represented as follows: (4) (5) The relationship between the peak strength and the corresponding in-plane displacement is represented as follows: (6) (7) The relationship between the residual strength and the corresponding in-plane displacement is represented as follows: = 0.85 (8) (9) wherein, is the yield strength; is the peak strength; is the residual strength; is the in-plane displacement corresponding to the yield strength; is the in-plane displacement corresponding to the peak strength; is the in-plane displacement corresponding to the residual strength; is the axial stiffness; is the stiffening segment stiffness of the equivalent strut load-displacement curve of the infilled wall; is the strut angle of the infilled wall.

8. The method according to claim 7, wherein the method is characterized by The specific steps of step five are as follows: First step, segment the yield curve and calculate the slope of the broken line: from the three curves of formula (1), (2), (3) select the curve with the maximum curvature, in the first quadrant, according to the specified angle, evenly divide the curve into segments, Take an odd number, the angle of each segment is ; take as the horizontal coordinate, as the vertical coordinate, where is the in-plane load, is the in-plane peak load, is the out-of-plane bending moment, is the out-of-plane maximum bending moment, by calculating the slope of each segment of the broken line, the slope of the broken line is obtained segment ; Second step, according to the yield curve broken line slope to determine the other two curve segmentation point: in the yield curve of broken line slope After, using these slopes from the curve both ends to the middle step by step, namely the other two curves in the case of keeping the slope unchanged, from both ends to the middle of the curve connecting points in turn, in order to determine the other two curve segmentation point; Third step, calculate actual load, bending moment and distance: after determining the three curves of the segmentation point and the corresponding slope, respectively multiplied by the load and reference bending moment , get actual load and actual bending moment , further calculate the corresponding curve of the fiber cross-sectional area, the stress and strain of the structure at different positions.

9. The method according to claim 8, wherein the method is characterized by The .

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